Radiation heat transfer analysis of a Czochralski furnace with a radiation shield

This paper reports on the radiation heat transfer from the melt in a Czochralski crystal growing furnace in the presence of a radiation shield The change of radiation heat transfer effects three basic areas, the cooling rate of the crystal, the bulk flow and the bulk temperature of the melt. The shield is installed above the melt to inhibit the heat transfer from the melt to the cooling crystal, allowing the crystal to grow 40% faster. Radiation is the primary mode of heat transfer in the furnace where the temperature to grow silicon crystals is around 1773K. The governing equations are the three-dimensional Navier Stokes equations in cylindrical coordinates for laminar flow, with the buoyancy term present, and the energy equation. The boundary conditions at the free surface of the melt are nonlinear due to the presense of the radiation. Instead of introducing the stream function to facilitate the solution, the Svanberg vorticity parameter, w/r, was introduced. The resulting equations were solved by an iterative process to yield the velocity distribution in the melt. Then these equations were used to solve the unsteady state energy equation. The radiation view factors were calculated by using a program called CONFACII. The temperature values thus obtained were used for the buoyancy terms in the Navier Stokes equations